Theoretical analysis of transient solution phase concentration field in a porous composite electrode with time-dependent flux boundary condition

2021 ◽  
Author(s):  
Long Zhou ◽  
Mohammad Parhizi ◽  
Ankur Jain
Keyword(s):  
Boundary Condition ◽  
Theoretical Analysis ◽  
Composite Electrode ◽  
Concentration Field ◽  
Solution Phase ◽  
Time Dependent ◽  
Transient Solution ◽  
Porous Composite ◽  
Flux Boundary Condition ◽  
Phase Concentration

Double dispersion effects on non-Darcy free convective boundary layer flow of a nanofluid over vertical frustum of a cone with convective boundary condition

2017 ◽  
Vol 6 (4) ◽  
Author(s):  
Ch. RamReddy ◽  
Ch. Venkata Rao
Keyword(s):  
Boundary Condition ◽  
Volume Fraction ◽  
Concentration Field ◽  
Convective Boundary Condition ◽  
Complex Problem ◽  
Convection Flow ◽  
Surface Drag ◽  
Convective Boundary ◽  
Flux Boundary Condition ◽  
Double Dispersion

AbstractIn this paper, a numerical analysis is performed to investigate the effects of double dispersion and convective boundary condition on natural convection flow over vertical frustum of a cone in a nanofluid saturated non-Darcy porous medium. In addition, Brownian motion and thermophoresis effects have taken into consideration, and the uniform wall nanoparticle condition is replaced with the zero nanoparticle mass flux boundary condition to execute physically applicable results. For this complex problem, the similarity solution does not exist and hence suitable non-similarity transformations are used to transform the governing equations along with the boundary conditions into non-dimensional form. The Bivariate Pseudo-Spectral Local Linearisation Method (BPSLLM) is used to solve the reduced non-similar, coupled partial differential equations. To test the accuracy of proposed method, the error analysis and convergence tests are conducted. The effect of flow influenced parameters on non-dimensional velocity, temperature, nanoparticle volume fraction, regular concentration field as well as on the surface drag, heat transfer, nanoparticle and regular mass transfer rates are analyzed.

scholarly journals Tear film dynamics with evaporation, wetting, and time-dependent flux boundary condition on an eye-shaped domain

2014 ◽  
Vol 26 (5) ◽  
pp. 052101 ◽  
Author(s):  
Longfei Li ◽  
R. J. Braun ◽  
K. L. Maki ◽  
W. D. Henshaw ◽  
P. E. King-Smith
Keyword(s):  
Boundary Condition ◽  
Tear Film ◽  
Time Dependent ◽  
Flux Boundary Condition ◽  
Shaped Domain

scholarly journals Generalized analytical solution for advection-dispersion equation in finite spatial domain with arbitrary time-dependent inlet boundary condition

2011 ◽  
Vol 8 (2) ◽  
pp. 4099-4120
Author(s):  
J.-S. Chen ◽  
C.-W. Liu
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Concentration Field ◽  
Generalized Solution ◽  
Spatial Domain ◽  
Time Dependent ◽  
Hydrodynamic Dispersion ◽  
Arbitrary Time ◽  
Special Cases ◽  
Inlet Boundary Condition

Abstract. This study presents a generalized analytical solution for one-dimensional solute transport in finite spatial domain subject to arbitrary time-dependent inlet boundary condition. The governing equation includes terms accounting for advection, hydrodynamic dispersion, linear equilibrium sorption and first order decay processes. The generalized analytical solution is derived by using the Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate. Several special cases are presented and compared to illustrate the robustness of the derived generalized analytical solution. Result shows an excellent agreement. The analytical solutions of the special cases derived in this study have practical applications. Moreover, the derived generalized solution which consists an integral representation is evaluated by the numerical integration to extend its usage. The developed generalized solution offers a convenient tool for further development of analytical solution of specified time-dependent inlet boundary conditions or numerical evaluation of the concentration field for arbitrary time-dependent inlet boundary problem.

Development of a CFD Boundary Condition to Model Transient Vapor Absorption in the Respiratory Airways

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Geng Tian ◽  
P. Worth Longest
Keyword(s):  
Boundary Condition ◽  
Steady State ◽  
Transient Absorption ◽  
Realistic Model ◽  
Time Dependent ◽  
Cfd Simulations ◽  
Wall Model ◽  
Flux Boundary Condition ◽  
Analytical Expression ◽  
Conducting Airways

The absorption of moderately and highly soluble vapors into the walls of the conducting airways was previously shown to be a transient process over the timescale of an inhalation cycle. However, a boundary condition to predict the transient wall absorption of vapors in CFD simulations does not exist. The objective of this study was to develop and test a boundary condition that can be used to predict the transient absorption of vapors in CFD simulations of transport in the respiratory airways. To develop the boundary condition, an analytical expression for the concentration of an absorbed vapor in an air-mucus-tissue-blood (AMTB) model of the respiratory wall was developed for transient and variable air-phase concentrations. Based on the analytical expression, a flux boundary condition was developed at the air-mucus interface as a function of the far-field air-phase concentration. The new transient boundary condition was then implemented to predict absorption in a realistic model of the extrathoracic nasal airways through the larynx (nasal-laryngeal geometry). The results of the AMTB wall model verified that absorption was highly time dependent over the timescale of an inhalation cycle (approximately 1–2 s). At 1 s, transient conditions resulted in approximately 2–3 times more uptake in tissue and 20–25 times less uptake in blood than steady state conditions for both acetaldehyde and benzene. Application of this boundary condition to computational fluid dynamics simulations of the nasal-laryngeal geometry showed, as expected, that transient absorption significantly affected total deposition fractions in the mucus, tissue, and blood. Moreover, transient absorption was also shown to significantly affect the local deposition patterns of acetaldehyde and benzene. In conclusion, it is recommended that future analyses of vapors in the conducting airways consider time-dependent wall absorption based on the transient flux boundary condition developed in this study. Alternatively, a steady state absorption condition may be applied in conjunction with correction factors determined from the AMTB wall model.

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